In the figure an ideal gas changes is state from state A to state C by two paths ABC and AC.
(a) Find the path along which the work done is least.
(b) The internal energy of the gas at A is 10 J and the amount of heat supplied to change its state to C through the path AC is 200 J. Calculate the internal energy at C.
(c) The internal energy of the gas at state B is 20 J. Fid the amount of the heat supplied to gas to go from A to B.

Explanation

(a) Path ABC:
`DeltaW_(ArarrB)=0`(since volume is constant)
`DeltaW_(BrarrC)=`area below the process `BrarrC`
`=15xx(6-2)=60J`
`DeltaW_(ABC)=DeltaW_(AB)=DeltaW_(BC)=0+60=60J`
Path AC:
`DeltaW_(ArarrC)=` area below the process `ArarrC`
`=(1)/(2)(5+15)(6-2)=40J`
`DeltaW_(AC) lt DeltaW_(ABC)`
(b) `U_A=10J`,`DeltaQ_(AC)=200J`,`DeltaW_(AC)=40J`
`DeltaQ_(AC)=DeltaU_(AC)+DeltaW_(AC)=U_C-U_A+DeltaW`
`200=U_C-10+40impliesU_C=170J`
(c) `DeltaQ_(AB)=DeltaU_(AB)+DeltaW_(AB)=U_B-U_A+0`
`=20-10=10J`